Remarque 7.3.14 Voir remarque 7.2.2 pour les restritions sur la portée de e lemme.
Dém. Soit z ∈ Kn. Parhypothèse zk = ϕk◦ · · · ◦ϕ0(z) ∈D, pour tout k = 0, . . . , n. Ainsi, d'après le lemme 7.3.1, |arg(zk −tk+1)| ≤ π
2, k = 0, . . . , n−1. Alors, du lemme 7.3.10, il
vient ∀k ≤n−1,|argzk| ≤ π
c|argzk+1|.
Corollaire 7.3.15 Si c > π, laomposante limiteI0 := \
n∈N
Kn,0 est un segment de ladroite réelle (éventuellement réduit au point 1).
En partiulier sa dimension de Hausdor est 0 ou 1. Conjeture 7.3.16 C'est vrai aussi pour c >1.
Remarque 7.3.17 Il est failedevoir quetoutes lesomposantesonnexes de K∞ quisont envoyéesenun nombrenid'étapes surlaomposanteontenant lepoint 1esthoméomorphe à I0.
7.4 Lien entre le modèle et son origine
On espère établir un isomorphisme entre le modèle supposé et e qu'il est ensé mo-déliser en utilisant la théorie de renormalisation des fontions presques paraboliques (voir notamment[36℄, [13℄).
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